Question

Make a table with the domain of {2,3,4,5,6} and draw a graph of the absolute value function y = 2|x-4| + 3.

Answer 1

Table for y = 2|x-4| + 3 on domain {2,3,4,5,6} is given as:

x y

2 2|x-4| + 3 = 2|2-4| + 3 = 7

3 2|x-4| + 3 = 2|3-4| + 3 = 5

4 2|x-4| + 3 = 2|4-4| + 3 = 3

5 2|x-4| + 3 = 2|5-4| + 3 = 5

6 2|x-4| + 3 = 2|6-4| + 3 = 7

The graph of the absolute value function y = 2|x-4| + 3 for the given domain is attached.

Explanation:

The absolute value parent function, written as function(x) = | x |, is defined as:

|x| = x and |-x| = x

In our case;

For x = 2

y = 2|x-4| + 3

= 2|2-4| + 3

= 2|-2| + 3

= 2*2 + 3

= 4 + 3

= 7

Similarly, for all other values of x in the given domain, value of y can be calculated.

Answer 2

In the attachment.

Explanation:

`|a|=\left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a<0\end{array}\right`

Put each value of x from the set {2, 3, 4, 5, 6}

to the equation y = 2|x - 4| + 3:

x = 2 → y = 2|2 - 4| + 3 = 2|-2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (2, 7)

x = 3 → y = 2|3 - 4| + 3 = 2|-1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (3, 5)

x = 4 → y = 2|4 - 4| + 3 = 2|0| + 3 = 2(0) + 3 = 0 + 3 = 3 → (4, 3)

x = 5 → y = 2|5 - 4| + 3 = 2|1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (5, 5)

x = 6 → y = 2|6 - 4| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (6, 7)

Mark the points in the coordinates system.

The domain is only five numbers, therefore the graph of this function is only five points.